DIRECTIONS for questions 1 and 2: These questions are based on the following data.
Rama went to the market and bought some apples, mangoes and bananas. He bought 42 fruits in all. The number of bananas is less than half the number of apples; the number of mangoes is more than one-third the number of apples and the number of mangoes is less than three-fourths the number of bananas.
1. How many apples did Rama buy?
(1) 20 (2) 23 (3) 26 (4) 28
2. How many bananas did Rama buy?
(1) 8 (2) 9 (3) 10 (4) 11
DIRECTIONS for questions 3 to 5: These questions are based on the data given below.
Everyday, Saddam, the office attender fetches water for the office in container A which has certain rated capacity.
However, because of a dent at the bottom of the container, only 80% of the rated capacity of the container can be used to fill water. This water is transferred periodically into a smaller container B - for people in the office to use this water for drinking. There is an outlet (a faucet) in B from which water is let out. Since the faucet is fixed at a level above the base of B, water upto 10% of the rated capacity of B cannot be let out through the faucet. Everyday in the morning, after Saddam fetches water in container A, he cleans B and fills B to the brim by pouring water from A into B. Whenever the water level falls to the faucet level in B, he again fills B to the brim by pouring water from A into B. The questions in this set are independent of each other.
3. On a particular day, Saddam finds that he filled B five times (including the first time) and at the end of the day, A was empty. The water level in B reached the faucet level. What is the ratio of the rated capacities of A and B?
(1) 4.6 : 1 (2) 5 : 1 (3) 5.75 : 1 (4) 6.25 : 1
4. If Saddam gets the dent in container A removed (so that water can be fetched in this container to its rated capacity) how many times can he fill container B (including the first time in the morning) given that the rated capacities of the two containers are in the ratio 10 : 1?
(1) 9 times (2) 10 times (3) 12 times (4) 11 times
5. Saddam gets the dent in container A removed. He also gets the faucet in container B refixed so that all the water filled into B can be used. He keeps filling B from A everytime B gets emptied. After he pours out water from A into B the last time (i.e., A gets emptied), what percentage of B is empty? The ratio of the rated capacities of A and B is 7.5 : 1?
(1) 0% (2) 331/3% (3) 25% (4) 50%
DIRECTIONS for questions 6 and 7: These questions are based on the following data.
Amar, Akbar and Anthony sold their three cycles manufactured in different years to Mr.Kishanlal. Mr.Kishanlal gave a total of Rs.1700 to the three and said that Amar should get about one-half of the total amount as his cycle was used less. Akbar’s cycle being used more than Amar’s, he should get about one-third of the total amount and the last one gets about one-ninth. Each individual gets his amount only in denominations of Rs.100.
6. What is the difference between the amounts received by Amar and Anthony?
(1) Rs.900 (2) Rs.700 (3) Rs.800 (4) Rs.600
7. The amount that Amar has is how much more than what Akbar and Anthony together have?
(1) Rs.200 (2) Rs.300 (3) Rs.100 (4) Rs.400
Directions for questions 8 to 12: Select the correct alternative from the given choices.
8. A, B and C start running simultaneously from the points P, Q and R respectively on a circular track. The distance (when measured along the track) between any two of the three points P, Q and R is L and the ratio of the speeds of A, B and C is 1 : 2 : 3. If A and B run in opposite directions while B and C run in the same direction, what is the distance run by C before A , B and C meet for the first time?
(1)10/3L (2)11/3 L
(3) All three of them will never meet. (4) Cannot be determined
9. A circle of radius 1cm circumscribes a square. A dart is thrown such that it falls within the circle. What is the
probability that it falls outside the square?
(1) 1/2π (2) (2π - 1) /2π (3) (π - 1) /π (4) (π - 2) /π
10. Fifteen boys went to collect berries and returned with a total of 80 berries among themselves. What is the minimum number of pairs of boys that must have collected the same number of berries?
(1) 0 (2) 1 (3) 2 (4) 3
11. A cube of edge 12 ft is placed on the floor with one of its faces touching a wall. A ladder of length 35 ft is resting against that wall and is touching an edge of the cube. Find the height at which the top end of the ladder touches the wall, given that it is more than the distance of the foot of the ladder from the wall?
(1) 11 ft (2) 23 ft (3) 21 ft (4) 28 ft
12. Two circles touch each other externally. One of the circles is 300% more in area than the other. If A is the centre of the larger circle and BC is the diameter of the smaller circle and either AB or AC is a tangent to the smaller circle, then find the ratio of the area of the triangle ABC to that of the smaller circle?
(1) 2 : π (2) 3 : π (3) 2 2 : π (4) π : 42
DIRECTIONS for questions 13 and 14: Select the correct alternative from the given choices.
13. a1, a2, a3, a4 and a5 are five natural numbers. Find the number of ordered sets (a1, a2, a3, a4, a5) possible such that a1 +a2 + a3 + a4 + a5 = 64.
(1) 64C5 (2) 63C4 (3) 65C4 (4) None of these
14. In the above question if a1, a2, a3, a4 and a5 are non-negative integers then find the number of ordered sets (a1, a2, a3, a4 and a5) that are possible.
(1) 64C5 (2) 63C4 (3) 68C4 (4) None of these
DIRECTIONS for questions 15 to 17: Each question gives certain information followed by two quantities A and B.
Compare A and B, and then
Mark 1 if A > B
Mark 2 if B > A
Mark 3 if A = B
Mark 4 if the relationship cannot be determined from the given data.
15. A baker had a certain number of boxes and a certain number of cakes with him. Initially he distributed all the cakes equally among all the boxes and found that there was no cake left without a box. He later found that he had one more box with him and so he redistributed all the cakes equally among all the boxes and found that there was one cake less per box than initially and one cake was left without a box with the baker.
A. The number of cakes per box in the first case.
B. The total number of boxes with the baker.
16. A trader gives a discount of r% and still makes a profit of r%. A second trader marks up his goods by r% and gives a discount of r%.
A. The cost price of the first trader.
B. The cost price of the second trader.
17. A piece of work is carried out by a group of men, all of equal capacity, in such a way that on the first day one man works and on every subsequent day one additional man joins the work. A group of women, all of equal capacity is engaged to carry out a second piece of work with ten women starting the work on the first day and one woman leaving the work at the end of everyday. The second piece of work is thrice as time consuming as the first piece of work while each man is thrice as efficient as each woman. It is known that one man working alone can complete the first piece of work in 6 days.
A. Number of days in which the first piece of work is completed.
B. Number of days in which the second piece of work is completed.
DIRECTIONS for questions 18 and 19: Select the correct alternative from the given choices.
18. A number when divided by a certain divisor, left a remainder of 8. When the same number was multiplied by 12 and then divided by the same divisor, the remainder is 12. How many such divisors are possible?
(1) 1 (2) 2 (3) 4 (4) 5
19. Consider the equation x² + y² + z² = 1. Let (x1, y1, z1) and (x2, y2, z2) be two sets of values of (x, y, z) satisfying the given equation and let A = (x1 – x2)² + (y1 – y2) ² + (z1 – z2)². What is the maximum possible value that A can assume?(assume that all the quantities involved are real numbers)
(1) 1 (2) 2 (3) 4 (4) 6
Note Answers of Above Quant Injection are here
Showing posts with label Quant Injection. Show all posts
Showing posts with label Quant Injection. Show all posts
Thursday, June 18, 2009
Thursday, May 28, 2009
Very Good Quantitative Tips and Tricks for all MBA entrance Tests
Dear Friends,
I am back with all new Quantitative Aptitude tips and tricks. As we all now that if we know the basic tricks of quantitative maths we can easily apply those tricks in Data Interpretation as well. So I have collected all the small but effective tricks of mathematics to make your calculations quite faster than ever. These tricks are like one get a treasure and you can clear any mathematical problem asked in any MBA entrance exam such as CAT, XAT, SNAP, FMS, MAT, MHCET etc.
So pals get these tricks as early as possible and do try these tricks with examples because cramming cannot take you anywhere. You need to do practice with these tricks to get perfection in them.
At last all the best and I shall be back tomorrow with new quantitative questions and RC passages as well as sentence correction exercise.
Get Maths tips and tricks at
http://rapidshare.com/files/238256742/Quant_Points.rar
Thank You.
I am back with all new Quantitative Aptitude tips and tricks. As we all now that if we know the basic tricks of quantitative maths we can easily apply those tricks in Data Interpretation as well. So I have collected all the small but effective tricks of mathematics to make your calculations quite faster than ever. These tricks are like one get a treasure and you can clear any mathematical problem asked in any MBA entrance exam such as CAT, XAT, SNAP, FMS, MAT, MHCET etc.
So pals get these tricks as early as possible and do try these tricks with examples because cramming cannot take you anywhere. You need to do practice with these tricks to get perfection in them.
At last all the best and I shall be back tomorrow with new quantitative questions and RC passages as well as sentence correction exercise.
Get Maths tips and tricks at
http://rapidshare.com/files/238256742/Quant_Points.rar
Thank You.
Monday, May 25, 2009
Quant Injection for 25th May 2009
Dear Friends,
I hope that you enjoyed solving seven mocks given by me. Send comments if you liked them. I am collecting more mock CAT tests so that you can have enough material to crack the toughest exam CAT. So here I give you a very good bunch of questions based on quantitative ability. It also contains XAT 2008 and 2009 papers. Go and get it downloaded.
http://rapidshare.com/files/237108061/Good_Quant_Problems.rar
Thanks.
I hope that you enjoyed solving seven mocks given by me. Send comments if you liked them. I am collecting more mock CAT tests so that you can have enough material to crack the toughest exam CAT. So here I give you a very good bunch of questions based on quantitative ability. It also contains XAT 2008 and 2009 papers. Go and get it downloaded.
http://rapidshare.com/files/237108061/Good_Quant_Problems.rar
Thanks.
Monday, May 18, 2009
Quant Injection for 17th May 2009
Dear Friends,
I hope that you are enjoying solving tests given by me. But folks, I am also a human being. It will cost you nothing if you appreciate me but it will motivate me to do more for you. If you like or hate anything do say it via a comment. I'll accept it as it will be. Anyway, Here I am uploading Quant Injection for 17th May 2009.
Instructions:
1) The duration of this test is 50 minutes and the test is meant to be taken in one-go without any break(s).
2) This test has 25 questions. Each question carries +4 marks on answering correctly.
3) Wrong answer(s) carries negative mark that is progressive. For the 1st two wrong answers the negative marking is -1 each, and -1 more on the previous for each subsequent wrong answer. E.g. 5 wrong answers attract penalty of (-1*2 – 2-3-4 = -11 marks).
4) Use of slide rule, log tables and calculators is not permitted.
5) Use the blank space in the question paper for the rough work.
(1) There are 12 towns grouped into four zones with three towns per zone. It is intended to connect the towns with telephone lines such that every two towns are connected with three direct lines if they belong to the same zone, and with only one direct line otherwise. How many direct telephone lines are required?
(a) 72 (b) 90 (c) 96 (d) 108 (e) 120
(2) If logx/log10 - log√x/log10 = 2log10/logx, then a possible value of x is given by
(a) 10 (b) 1/100 (c) 1/1000 (d) 100 (e) exactly two of the foregoing
(3) ABCDEF is a regular hexagon. Points P and Q are on AB and CD respectively such that AP/BP = CQ/QD = 3. What is the ratio area(BPDC)/area(ABCDEF)?
(a) 5:24 (b) 11:54 (c) 19:96 (d) 5:27 (e) 7:32
(4) The set M consists of p consecutive integers with sum 2p. The set N consists of 2p consecutive integers with sum p. The difference between the largest elements of M and N is 9. Then p is
(a) 17 (b) 36 (c) 9 (d) 27 (e) 21
(5) The angle between the hour and minute hands of a standard 12-hour clock is exactly 1 degree. The time is an integral number n of minutes after noon (where 0 < ab =" a," bc =" b," dx =" (a)" x =" -|a|b,"> 0 (d) a – xb ≤ 0 (e) a > b
(12) A lecture room has a rectangular array of chairs. There are 6 boys in each row and 8 girls in each column. 15 chairs are unoccupied. How many distinct pairs of (row, column) can this lecture room have?
(a) 4 (b) 2 (c) 6 (d) 3 (e) 5
(13) Consider two different cloth cutting processes. In the first one, n circular cloth pieces are cut from a square cloth piece of side s in the following steps: the original square of side s is divided into n smaller squares, not necessarily of the same size; then a circle of maximum possible area is cut from each of the smaller squares. In the second process, only one circle of maximum possible area is cut from the square of side s and the process ends there. The cloth pieces remaining after cutting the circles are scrapped in both the processes. The ratio of the total scrap cloth generated in the former to that in the latter is: (∏ = circumference of the circle/diameter of the circle)
(a) 1:1 (b) √2:1 (c) n(4-∏)/(4n-∏) (d) (4n-∏)/n(4-∏) (e) 1:√2
(14) The remainder when x^100 (x > 0) is divided by x^3 + 1 is
(a) x^2 + x + 1 (b) x (c) x^3 – x + 1 (d) 2x^2 – 1 (e) -x
(15) Two stations A and B are 920 km apart. A train T1, which stops for 5 minutes in every town-station and for 3 minutes in every village-station started from A with a speed of 60km/h towards B and at the same time a train T2 with a speed of 80km/h which does not stop in any intermediate station started from B towards A. They met at C which is 560 km away from B. If the number of town-stations between A and C is less than the number of village-stations, then at least how many stations - town or village - are there between A and C? Assume T1 stops only at town or village-stations.
(a) 12 (b) 13 (c) 16 (d) 18 (e) 20
(16) What is the area enclosed by the graph of |x - 60| + |y| = |x/4|?
(a) 120 (b) 240 (c) 360 (d) 480 (e) 720
(17) In a triangle PQR, PQ = QR, S and T are points on PR and PQ respectively such that RQ = QS = ST = TP. Then
(a) (75, 90) (b) (105, 120) (c) (135, 150) (d) (120, 135) (e) none of the foregoing
(18) a, b, c, d, e, f, g are non-negative such that a+b+c+d+e+f+g = 1. Then the minimum value of max(a+b+c, b+c+d, c+d+e, d+e+f, e+f+g) is
(a) 1/3 (b) 3/7 (c) 1 (d) 0 (e) none of the foregoing
(19) Let the length of common tangents when two circles cut each other at a right angle be x. The length of common tangent when these two circles are separated so as to touch each other is
(a) √2x (b) (√2+1)x (c) √3x (d) (√3+1)x (e) (√5+1)x/2
(20) If a/(b+c) + b/(c+a) + c/(a+b) = 1, then (a^3 + b^3 + c^3)/abc is
(a) 0 (b) 1 (c) -3 (d) 3 (e) none of the foregoing
(21) Nokia manufactures mobile handsets and marks a price which is 8 times the manufacturing price, and prints it on the handset. They sell it to a distributor at a certain discount. The distributor then sells it to the wholesaler and offers him a discount equal to 3/4th of the discount that he received from the manufacturer. The wholesaler then sells it to the retailer at a discount equal to 2/3rd of the discount he received from the distributor. The retailer finally sells it to the customer at a discount equal to 1/2 the discount that he received from the wholesaler. If all the discounts are given on the price printed on the box and if the wholesaler made a profit of 50%, then who made the least profit?
(a) Manufacturer (b) Distributor (c) Wholesaler (d) Retailer (e) can not be determined
(22) Given a set of n rays in a plane, define a reversal as the operation of reversing precisely one ray and obtaining a new set of rays. If all the rays are reversed after 42 operations, then n can be
(a) 21 (b) 23 (c) 41 (d) 24 (e) At least two of the foregoing
(23) Quadrilateral ABCD is inscribed in a circle with diameter AD = 4. If sides AB=BC = 1 , then CD equals
(a) 5/2 (b) 4 (c) 3 (d) 5 (e) 7/2
(24) A task is assigned to a group of 11 men, not all of whom have the same capacity to work. Every day exactly 2 men out of the group work on the task, with no pair of men working together twice. Even after all the possible pairs have worked once, all the men together had to work for exactly one day more to finish the task. What is the number of days that will be required for all the men working together to finish the job.
(a) 11 (b) 21 (c) 33 (d) 12 (e) none of the foregoing
(25) Let x = (n^4 + 256 + 4n(n^2 + 16))/(n+4)^2. If 4 <= n^2 <= 49 then, (a) 12 <= x <= 147 (b) 28 <= x <= 95 (c) 12 <= x <= 37 (d) 12 <= x <= 95 (e) 28 <= x <= 147
*Note:- The answers for above test.
Thank You
I hope that you are enjoying solving tests given by me. But folks, I am also a human being. It will cost you nothing if you appreciate me but it will motivate me to do more for you. If you like or hate anything do say it via a comment. I'll accept it as it will be. Anyway, Here I am uploading Quant Injection for 17th May 2009.
Instructions:
1) The duration of this test is 50 minutes and the test is meant to be taken in one-go without any break(s).
2) This test has 25 questions. Each question carries +4 marks on answering correctly.
3) Wrong answer(s) carries negative mark that is progressive. For the 1st two wrong answers the negative marking is -1 each, and -1 more on the previous for each subsequent wrong answer. E.g. 5 wrong answers attract penalty of (-1*2 – 2-3-4 = -11 marks).
4) Use of slide rule, log tables and calculators is not permitted.
5) Use the blank space in the question paper for the rough work.
(1) There are 12 towns grouped into four zones with three towns per zone. It is intended to connect the towns with telephone lines such that every two towns are connected with three direct lines if they belong to the same zone, and with only one direct line otherwise. How many direct telephone lines are required?
(a) 72 (b) 90 (c) 96 (d) 108 (e) 120
(2) If logx/log10 - log√x/log10 = 2log10/logx, then a possible value of x is given by
(a) 10 (b) 1/100 (c) 1/1000 (d) 100 (e) exactly two of the foregoing
(3) ABCDEF is a regular hexagon. Points P and Q are on AB and CD respectively such that AP/BP = CQ/QD = 3. What is the ratio area(BPDC)/area(ABCDEF)?
(a) 5:24 (b) 11:54 (c) 19:96 (d) 5:27 (e) 7:32
(4) The set M consists of p consecutive integers with sum 2p. The set N consists of 2p consecutive integers with sum p. The difference between the largest elements of M and N is 9. Then p is
(a) 17 (b) 36 (c) 9 (d) 27 (e) 21
(5) The angle between the hour and minute hands of a standard 12-hour clock is exactly 1 degree. The time is an integral number n of minutes after noon (where 0 < ab =" a," bc =" b," dx =" (a)" x =" -|a|b,"> 0 (d) a – xb ≤ 0 (e) a > b
(12) A lecture room has a rectangular array of chairs. There are 6 boys in each row and 8 girls in each column. 15 chairs are unoccupied. How many distinct pairs of (row, column) can this lecture room have?
(a) 4 (b) 2 (c) 6 (d) 3 (e) 5
(13) Consider two different cloth cutting processes. In the first one, n circular cloth pieces are cut from a square cloth piece of side s in the following steps: the original square of side s is divided into n smaller squares, not necessarily of the same size; then a circle of maximum possible area is cut from each of the smaller squares. In the second process, only one circle of maximum possible area is cut from the square of side s and the process ends there. The cloth pieces remaining after cutting the circles are scrapped in both the processes. The ratio of the total scrap cloth generated in the former to that in the latter is: (∏ = circumference of the circle/diameter of the circle)
(a) 1:1 (b) √2:1 (c) n(4-∏)/(4n-∏) (d) (4n-∏)/n(4-∏) (e) 1:√2
(14) The remainder when x^100 (x > 0) is divided by x^3 + 1 is
(a) x^2 + x + 1 (b) x (c) x^3 – x + 1 (d) 2x^2 – 1 (e) -x
(15) Two stations A and B are 920 km apart. A train T1, which stops for 5 minutes in every town-station and for 3 minutes in every village-station started from A with a speed of 60km/h towards B and at the same time a train T2 with a speed of 80km/h which does not stop in any intermediate station started from B towards A. They met at C which is 560 km away from B. If the number of town-stations between A and C is less than the number of village-stations, then at least how many stations - town or village - are there between A and C? Assume T1 stops only at town or village-stations.
(a) 12 (b) 13 (c) 16 (d) 18 (e) 20
(16) What is the area enclosed by the graph of |x - 60| + |y| = |x/4|?
(a) 120 (b) 240 (c) 360 (d) 480 (e) 720
(17) In a triangle PQR, PQ = QR, S and T are points on PR and PQ respectively such that RQ = QS = ST = TP. Then
(a) (75, 90) (b) (105, 120) (c) (135, 150) (d) (120, 135) (e) none of the foregoing
(18) a, b, c, d, e, f, g are non-negative such that a+b+c+d+e+f+g = 1. Then the minimum value of max(a+b+c, b+c+d, c+d+e, d+e+f, e+f+g) is
(a) 1/3 (b) 3/7 (c) 1 (d) 0 (e) none of the foregoing
(19) Let the length of common tangents when two circles cut each other at a right angle be x. The length of common tangent when these two circles are separated so as to touch each other is
(a) √2x (b) (√2+1)x (c) √3x (d) (√3+1)x (e) (√5+1)x/2
(20) If a/(b+c) + b/(c+a) + c/(a+b) = 1, then (a^3 + b^3 + c^3)/abc is
(a) 0 (b) 1 (c) -3 (d) 3 (e) none of the foregoing
(21) Nokia manufactures mobile handsets and marks a price which is 8 times the manufacturing price, and prints it on the handset. They sell it to a distributor at a certain discount. The distributor then sells it to the wholesaler and offers him a discount equal to 3/4th of the discount that he received from the manufacturer. The wholesaler then sells it to the retailer at a discount equal to 2/3rd of the discount he received from the distributor. The retailer finally sells it to the customer at a discount equal to 1/2 the discount that he received from the wholesaler. If all the discounts are given on the price printed on the box and if the wholesaler made a profit of 50%, then who made the least profit?
(a) Manufacturer (b) Distributor (c) Wholesaler (d) Retailer (e) can not be determined
(22) Given a set of n rays in a plane, define a reversal as the operation of reversing precisely one ray and obtaining a new set of rays. If all the rays are reversed after 42 operations, then n can be
(a) 21 (b) 23 (c) 41 (d) 24 (e) At least two of the foregoing
(23) Quadrilateral ABCD is inscribed in a circle with diameter AD = 4. If sides AB=BC = 1 , then CD equals
(a) 5/2 (b) 4 (c) 3 (d) 5 (e) 7/2
(24) A task is assigned to a group of 11 men, not all of whom have the same capacity to work. Every day exactly 2 men out of the group work on the task, with no pair of men working together twice. Even after all the possible pairs have worked once, all the men together had to work for exactly one day more to finish the task. What is the number of days that will be required for all the men working together to finish the job.
(a) 11 (b) 21 (c) 33 (d) 12 (e) none of the foregoing
(25) Let x = (n^4 + 256 + 4n(n^2 + 16))/(n+4)^2. If 4 <= n^2 <= 49 then, (a) 12 <= x <= 147 (b) 28 <= x <= 95 (c) 12 <= x <= 37 (d) 12 <= x <= 95 (e) 28 <= x <= 147
*Note:- The answers for above test.
Thank You
Quant Injection for 15th May 2009
Dear Pals,
Here I give another injection of Quantitative Aptitude. Enjoy it and do comment if you like it.
http://rapidshare.com/files/234121740/Quant_Test_2.rar
Note:- The answers for above test.
Thank You
Here I give another injection of Quantitative Aptitude. Enjoy it and do comment if you like it.
http://rapidshare.com/files/234121740/Quant_Test_2.rar
Note:- The answers for above test.
Thank You
Thursday, May 14, 2009
Quant Injection for 13th May 2009
Dear Pals,
Actually there were some diagrams in the test, So I was not able to upload on my blog but I've given the link so you can download the test and also save it on your computer for future reference.
http://rapidshare.com/files/232606015/QuantTest1.rar
*Note:- The answers for the above Quant Questions will be updated tomorrow.
Thank You.
Actually there were some diagrams in the test, So I was not able to upload on my blog but I've given the link so you can download the test and also save it on your computer for future reference.
http://rapidshare.com/files/232606015/QuantTest1.rar
*Note:- The answers for the above Quant Questions will be updated tomorrow.
Thank You.
Tuesday, May 12, 2009
Quant Injection for 11th May 2009
There are 19 questions. Solve them according to your own timing. Answers will be given after 24 hours i.e. with next Quant Injection
DIRECTIONS for questions 1 and 2: These questions are based on the following data.
Rama went to the market and bought some apples, mangoes and bananas. He bought 42 fruits in all. The number of bananas is less than half the number of apples; the number of mangoes is more than one-third the number of apples and the number of mangoes is less than three-fourths the number of bananas.
1. How many apples did Rama buy?
(1) 20 (2) 23 (3) 26 (4) 28
2. How many bananas did Rama buy?
(1) 8 (2) 9 (3) 10 (4) 11
DIRECTIONS for questions 3 to 5: These questions are based on the data given below.
Everyday, Saddam, the office attender fetches water for the office in container A which has certain rated capacity.
However, because of a dent at the bottom of the container, only 80% of the rated capacity of the container can be used to fill water. This water is transferred periodically into a smaller container B - for people in the office to use this water for drinking. There is an outlet (a faucet) in B from which water is let out. Since the faucet is fixed at a level above the base of B, water upto 10% of the rated capacity of B cannot be let out through the faucet. Everyday in the morning, after Saddam fetches water in container A, he cleans B and fills B to the brim by pouring water from A into B. Whenever the water level falls to the faucet level in B, he again fills B to the brim by pouring water from A into B. The questions in this set are independent of each other.
3. On a particular day, Saddam finds that he filled B five times (including the first time) and at the end of the day, A was empty. The water level in B reached the faucet level. What is the ratio of the rated capacities of A and B?
(1) 4.6 : 1 (2) 5 : 1 (3) 5.75 : 1 (4) 6.25 : 1
4. If Saddam gets the dent in container A removed (so that water can be fetched in this container to its rated capacity) how many times can he fill container B (including the first time in the morning) given that the rated capacities of the two containers are in the ratio 10 : 1?
(1) 9 times (2) 10 times (3) 12 times (4) 11 times
5. Saddam gets the dent in container A removed. He also gets the faucet in container B refixed so that all the water filled into B can be used. He keeps filling B from A everytime B gets emptied. After he pours out water from A into B the last time (i.e., A gets emptied), what percentage of B is empty? The ratio of the rated capacities of A and B is 7.5 : 1?
(1) 0% (2) 331/3% (3) 25% (4) 50%
DIRECTIONS for questions 6 and 7: These questions are based on the following data.
Amar, Akbar and Anthony sold their three cycles manufactured in different years to Mr.Kishanlal. Mr.Kishanlal gave a total of Rs.1700 to the three and said that Amar should get about one-half of the total amount as his cycle was used less. Akbar’s cycle being used more than Amar’s, he should get about one-third of the total amount and the last one gets about one-ninth. Each individual gets his amount only in denominations of Rs.100.
6. What is the difference between the amounts received by Amar and Anthony?
(1) Rs.900 (2) Rs.700 (3) Rs.800 (4) Rs.600
7. The amount that Amar has is how much more than what Akbar and Anthony together have?
(1) Rs.200 (2) Rs.300 (3) Rs.100 (4) Rs.400
Directions for questions 8 to 12: Select the correct alternative from the given choices.
8. A, B and C start running simultaneously from the points P, Q and R respectively on a circular track. The distance (when measured along the track) between any two of the three points P, Q and R is L and the ratio of the speeds of A, B and C is 1 : 2 : 3. If A and B run in opposite directions while B and C run in the same direction, what is the distance run by C before A , B and C meet for the first time?
(1)10/3L (2)11/3 L
(3) All three of them will never meet. (4) Cannot be determined
9. A circle of radius 1cm circumscribes a square. A dart is thrown such that it falls within the circle. What is the
probability that it falls outside the square?
(1) 1/2π (2) (2π - 1) /2π (3) (π - 1) /π (4) (π - 2) /π
10. Fifteen boys went to collect berries and returned with a total of 80 berries among themselves. What is the minimum number of pairs of boys that must have collected the same number of berries?
(1) 0 (2) 1 (3) 2 (4) 3
11. A cube of edge 12 ft is placed on the floor with one of its faces touching a wall. A ladder of length 35 ft is resting against that wall and is touching an edge of the cube. Find the height at which the top end of the ladder touches the wall, given that it is more than the distance of the foot of the ladder from the wall?
(1) 11 ft (2) 23 ft (3) 21 ft (4) 28 ft
12. Two circles touch each other externally. One of the circles is 300% more in area than the other. If A is the centre of the larger circle and BC is the diameter of the smaller circle and either AB or AC is a tangent to the smaller circle, then find the ratio of the area of the triangle ABC to that of the smaller circle?
(1) 2 : π (2) 3 : π (3) 2 Ö2 : π (4) π : 4Ö2
DIRECTIONS for questions 13 and 14: Select the correct alternative from the given choices.
13. a1, a2, a3, a4 and a5 are five natural numbers. Find the number of ordered sets (a1, a2, a3, a4, a5) possible such that a1 +a2 + a3 + a4 + a5 = 64.
(1) 64C5 (2) 63C4 (3) 65C4 (4) None of these
14. In the above question if a1, a2, a3, a4 and a5 are non-negative integers then find the number of ordered sets (a1, a2, a3, a4 and a5) that are possible.
(1) 64C5 (2) 63C4 (3) 68C4 (4) None of these
DIRECTIONS for questions 15 to 17: Each question gives certain information followed by two quantities A and B.
Compare A and B, and then
Mark 1 if A > B
Mark 2 if B > A
Mark 3 if A = B
Mark 4 if the relationship cannot be determined from the given data.
15. A baker had a certain number of boxes and a certain number of cakes with him. Initially he distributed all the cakes equally among all the boxes and found that there was no cake left without a box. He later found that he had one more box with him and so he redistributed all the cakes equally among all the boxes and found that there was one cake less per box than initially and one cake was left without a box with the baker.
A. The number of cakes per box in the first case.
B. The total number of boxes with the baker.
16. A trader gives a discount of r% and still makes a profit of r%. A second trader marks up his goods by r% and gives a discount of r%.
A. The cost price of the first trader.
B. The cost price of the second trader.
17. A piece of work is carried out by a group of men, all of equal capacity, in such a way that on the first day one man works and on every subsequent day one additional man joins the work. A group of women, all of equal capacity is engaged to carry out a second piece of work with ten women starting the work on the first day and one woman leaving the work at the end of everyday. The second piece of work is thrice as time consuming as the first piece of work while each man is thrice as efficient as each woman. It is known that one man working alone can complete the first piece of work in 6 days.
A. Number of days in which the first piece of work is completed.
B. Number of days in which the second piece of work is completed.
DIRECTIONS for questions 18 and 19: Select the correct alternative from the given choices.
18. A number when divided by a certain divisor, left a remainder of 8. When the same number was multiplied by 12 and then divided by the same divisor, the remainder is 12. How many such divisors are possible?
(1) 1 (2) 2 (3) 4 (4) 5
19. Consider the equation x² + y² + z² = 1. Let (x1, y1, z1) and (x2, y2, z2) be two sets of values of (x, y, z) satisfying the given equation and let A = (x1 – x2)² + (y1 – y2) ² + (z1 – z2)². What is the maximum possible value that A can assume?(assume that all the quantities involved are real numbers)
(1) 1 (2) 2 (3) 4 (4) 6
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